@article {
author = {Mosadeq, Maysam},
title = {Dynamical Systems Implemented by Isomorphic Groups of Unitaries},
journal = {Sahand Communications in Mathematical Analysis},
volume = {},
number = {},
pages = {-},
year = {2023},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {10.22130/scma.2023.559758.1158},
abstract = {Let $\varphi:A\to B$ be an isomorphism of $C^*$-algebras and $I$ be an ideal of $A.$ Introducing the concepts of unitary equivalent and the implemented Finsler modules, we show that the $\frac{A}{I}$-module $\frac{E}{E_{I}}$ and the implemented $\frac{B}{\varphi(I)}$-module $\frac{F}{F_{\varphi(I)}}$ are unitary equivalent. We also, establish a one to one correspondence between the groups $U(E)$ and $U(F)$ of unitaries on full Finsler modules $E$ and $F,$ respectively. Finally, we explain regularized dynamical systems and apply the aforementioned one to one correspondenec to prove that each regularized dynamical system in $U(E)$ implements a regularized dynamical system in $U(F).$},
keywords = {$C^*$-Dynamical systems,generalized derivation,Finsler module,ternary derivation,one parameter group,unitary operator},
url = {https://scma.maragheh.ac.ir/article_703194.html},
eprint = {}
}